import git

# Open the repository
repo = git.Repo('/path/to/your/repo')

def get_lightweight_tags_for_annotated_tag(repo, annotated_tag_name):
    # Get the commit associated with the annotated tag
    annotated_tag = repo.tags[annotated_tag_name]
    if annotated_tag.tag:
        annotated_commit = annotated_tag.tag.commit
    else:
        raise ValueError(f"{annotated_tag_name} is not an annotated tag")

    # List all lightweight tags that point to the same commit
    lightweight_tags = []
    for tag in repo.tags:
        if tag.tag is None and tag.commit == annotated_commit:
            lightweight_tags.append(tag.name)

    return lightweight_tags

# Example usage
annotated_tag_name = 'annotated_tag1'
lw_tags = get_lightweight_tags_for_annotated_tag(repo, annotated_tag_name)
print(f"Lightweight tags for {annotated_tag_name}: {lw_tags}")